This is pretty much what happened to be in German class once in high school.

I had to prepare a presentation about two short books; One I was allowed to discuss based on a summary, one I should read myself. Ever the motivated pupil that I was, of course I did read it, and prepared the other from an interpretation found on the internet. The teacher thought I had read the other one

Azazeltje wrote:I am so lost on the math here - is he saying that random chance would lead to correct guesses from Group A two-thirds of the time? Why is that not 50/50?

Random chance will often give you close to 50/50, but not exactly. He's saying that if they get it wrong more than 2/3 of the time, that's worse than even random guessing is statistically likely to get, but between 1/3 and 2/3 is kind of in the range of possible outcomes of random guessing.

Statistics is an entire branch of mathematics dedicated to figuring out what's a statistically likely result given a certain condition, and what isn't. Zach didn't seem to apply any statistical knowledge here, so he just fudged it.

Azazeltje wrote:I am so lost on the math here - is he saying that random chance would lead to correct guesses from Group A two-thirds of the time? Why is that not 50/50?

Random chance will often give you close to 50/50, but not exactly. He's saying that if they get it wrong more than 2/3 of the time, that's worse than even random guessing is statistically likely to get, but between 1/3 and 2/3 is kind of in the range of possible outcomes of random guessing.

Statistics is an entire branch of mathematics dedicated to figuring out what's a statistically likely result given a certain condition, and what isn't. Zach didn't seem to apply any statistical knowledge here, so he just fudged it.

So under his test, if the Group A people guess correctly less than 50% of the time, the book fails, because its less than random chance - but the book only passes if they get better than 66%... so what happens to books that fall in the 51-65% range?

Azazeltje wrote:I am so lost on the math here - is he saying that random chance would lead to correct guesses from Group A two-thirds of the time? Why is that not 50/50?

Random chance will often give you close to 50/50, but not exactly. He's saying that if they get it wrong more than 2/3 of the time, that's worse than even random guessing is statistically likely to get, but between 1/3 and 2/3 is kind of in the range of possible outcomes of random guessing.

Statistics is an entire branch of mathematics dedicated to figuring out what's a statistically likely result given a certain condition, and what isn't. Zach didn't seem to apply any statistical knowledge here, so he just fudged it.

Oh I think I misunderstood your answer - you're saying that even tho the odds are 50/50, actual outcomes are likely to be scattered in between the 1/3-2/3 range - so the cutoff is just 66% - higher passes, lower fails - that makes a certain kind of logical sense, but i don't think thats actually whats intended - because if the odds are 50/50 (which we seem to agree thats the prescriptive calculation) it would be rare for the actual outcomes to be SO far off that they come out at 1/3 or 2/3... in fact, shouldn't that question itself be something stats can shine a light on? how likely it would be for the outcome to be X number of standard deviations away from the prescriptive value?

I'm clearly not a mathematician, so if anyone knows anything, don't be shy

As per the comic:
67%-100%: book passes the test
34%-66%: book fails the test
0%-33%: book is assigned for a class on philosophical modernism

(it broke my heart sightly to use 33/34/66/67, but I didn't want to make this more confusing than it needs to be)

Edit: and as I said, the actual figure of 1/3 to 2/3 is completely made up. Real experiments usually use much tighter error margins, which they calculate using statistics and math based on the number of measurements and other factors. So by using such a huge margin Zach is actually giving the book a really big chance to fail the test - or rather, it requires that the test would give such a clear answer that there's absolutely no doubt.